1. Field of the Invention
The present invention relates to an electromagnetic field intensity calculation apparatus and an electromagnetic field intensity calculation method. More particularly, the invention relates to an electromagnetic field intensity calculation apparatus and an electromagnetic field intensity calculation method that calculate the electromagnetic field intensity radiated from an electric circuit device at high speed while maintaining high accuracy.
Electromagnetic waves radiated from electric circuit devices interfere with other electromagnetic waves such as those of television and radio broadcasting, and strict regulations have come to be imposed on such radiation in various countries of the world. Examples of standards defining such regulations include the VCCI standards of Japan, the FCC standards of the U.S.A., and the VDE standards of Germany.
Various techniques such as shielding techniques and filtering techniques are used to meet these electromagnetic wave standards. When employing such techniques, it is necessary to carry out a simulation to quantitatively determine how much of the energy of the radiation the technique concerned can shield. A need therefore arises for an electromagnetic field intensity calculation apparatus that can simulate electromagnetic field intensities radiated from electric circuit devices with high accuracy.
2. Description of the Related Art
The strength of an electromagnetic field around an object of an arbitrary shape can be easily calculated using known theoretical equations, if the electric current flowing in each part of the object is known. Theoretically, this current value can be obtained by solving Maxwell""s electromagnetic wave equations under given boundary conditions. However, analytical solutions for an object of an arbitrary shape under complex boundary conditions are not available yet.
The methods, for obtaining the electric current, which are used in electromagnetic field intensity calculation apparatus today, all provide approximate solutions. At present, three kinds of approximate solution methods are known: the infinitesimal loop antenna approximation method, the distributed constant transmission line approximation method, and the moment method.
The infinitesimal loop antenna approximation method is a method in which the conductor connecting between a wave source circuit and a load circuit is treated as a loop antenna and, by assuming the electric current on the loop to be flat, the electric current is determined using a calculation technique of a lumped constant circuit. Calculation by the infinitesimal loop antenna approximation method is the simplest. However, since the calculation accuracy drops significantly under conditions in which the loop dimension becomes significant compared to the wavelength of electromagnetic radiation, this method is of very little use in practice.
The distributed constant transmission line approximation method is a method in which the electric current is obtained by applying a distributed constant transmission line equation to an object that can be approximated as a one-dimensional structure. Calculation by the distributed constant transmission line approximation method is relatively simple, with the required computation time and memory capacity only increasing almost proportionally to the number of elements to be analyzed; furthermore, phenomena such as reflection and resonance of the transmission line can also be analyzed. An analysis can therefore be done with high accuracy and at high speed for objects for which one dimensional approximations are possible. However, the distributed constant transmission line approximation method has a problem in that an analysis cannot be done for objects that cannot be approximated to one-dimensional structures.
The moment method is a method of solving an integral equation derived from Maxwell""s electromagnetic wave equations, and can handle three-dimensional objects of any shape. More specifically, the moment method divides an object into small elements (wires or surface patches or the like) and calculates the electric current flowing on each segment, thereby computing the electromagnetic field intensity. Since the moment method can handle three-dimensional objects of any shape, the design of electromagnetic field intensity calculation apparatus predominantly employs a configuration in which the strength of an electromagnetic field radiated from an electrical circuit device is calculated using the moment method.
Reference literature on the moment method includes the following.
H. N. Wang, J. H. Richmond and M. C. Gilreath: xe2x80x9cSinusoidal Reaction Formulation for Radiation and Scattering from Conducting Surface,xe2x80x9d IEEE TRANSACTIONS ANTENNAS PROPAGATION, AP-23, pp. 376-382, 1975.
In the moment method, as described for example in Japanese Patent Unexamined Publication Nos. 7-234890 and 7-302278 (U.S. Ser. No. 432,261) by the present inventor et al., a conductor constituting an electric circuit device, including a housing, cable, etc., is divided into small elements such as wires or surface patches. The mutual impedance between the elements and the self-impedance of each individual element (collectively called the mutual impedance Zij) are calculated using known mathematical equations from frequency values and the geometric data of the elements concerned, and the value of the mutual impedance Zij thus obtained is substituted into simultaneous equations describing a boundary condition for each element. By solving the simultaneous equations, the current flowing on each element is determined, from which the electromagnetic field intensity is calculated. When it is desired to increase the accuracy by taking into account the scattering of the electromagnetic field caused by a dielectric contained in the electric circuit device, the dielectric also is divided into small elements, and the mutual admittance Yij and mutual reaction Bij are calculated for each element in addition to the mutual impedance Zij; then, simultaneous equations containing a boundary condition for each element of the dielectric are solved.
In specifications defining EMC electromagnetic wave regulations, allowable values are specified for the regulated frequency range. For example, the VCCI standards, defining EMC electromagnetic wave regulations in Japan, stipulate the regulated frequency range of 30 MHz to 1 GHz and specify allowable values for that frequency range. Consider a transmission line on a printed circuit board as an example of an electric circuit device subject to the electromagnetic wave regulations. The transmission line sends an output of a driver (output circuit) to a receiver (receiving circuit). The output of the driver has a pulse-like voltage waveform. The components actually radiated from the transmission line, therefore, contain the fundamental frequency (f0) component of the clock, plus its harmonic components (f1, f2, . . . fn, . . . ) whose frequencies are integral multiples of the fundamental frequency. As a result, in an electromagnetic field intensity calculation apparatus, calculations for the simulation of electromagnetic field intensities must be performed on all the harmonic components generated from the transmission line and falling within the regulated frequency range. An electric field spectrum is obtained as a result of such simulation. The resulting electric field spectrum is a set of electric field intensities calculated at the respective frequencies by the electromagnetic field intensity calculation apparatus using the moment method. Accordingly, to obtain the electric field spectrum, the electromagnetic field intensity calculation by the moment method has to be performed for each frequency (each of the fundamental frequency and/or harmonic frequencies). That is, the calculation process has to be repeated for each frequency. This has lead to the problem that it takes a very long time for the prior art electromagnetic field intensity calculation apparatus to determine through simulation whether the EMC electromagnetic wave specifications are satisfied or not. For the calculation of mutual impedances, in particular, there has been the problem that the calculation takes an extremely long time because the amount of calculation is enormous.
Thus the prior art electromagnetic field intensity calculation apparatus employs a method that calculates the mutual impedance for xe2x80x9ceachxe2x80x9d frequency by carrying out known processing commonly used in the moment method for the calculation of the mutual impedance. The prior art electromagnetic field intensity calculation apparatus therefore has had the problem that processing involving a considerable amount of calculation has to be performed for each frequency. This problem becomes more serious when the mutual admittance or mutual reaction has to be obtained in addition to the mutual impedance.
An example of calculation time will be given below. The calculation time depends much on the shape of a three-dimensional object to be simulated. To give a rough value, when a three-dimensional object to be simulated was divided into elements consisting of 1000 surface patches, it took several hours to calculate the electromagnetic field intensity for each frequency. More specifically, it took several hours to calculate the mutual impedance, several minutes to calculate the simultaneous equations, and several minutes to calculate the electric field or magnetic field.
It is an object of the present invention to provide an apparatus for calculating an electromagnetic field intensity and a method of calculating the same, capable of calculating the strength of an electromagnetic field radiated from an electric circuit device at high speed while maintaining high accuracy.
According to the present invention, there is provided a method of calculating an electromagnetic field intensity, comprising the steps of: a) calculating approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting an electric circuit device and of the elements themselves, at an arbitrary frequency; and b) calculating the approximate values of the electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated in step a), thereby making it possible to evaluate the electromagnetic field intensity for the designated frequency.
According to the present invention, there is also provided an apparatus for calculating an electromagnetic field intensity, comprising: means for calculating approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting an electric circuit device and of the elements themselves, at an arbitrary frequency; and means for calculating the approximate values of the electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated by the approximation coefficients calculating means, thereby making it possible to evaluate the electromagnetic field intensity for the designated frequency.
According to the present invention, there is also provided a program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform method steps for calculating an electromagnetic field intensity, the method steps comprising: a) calculating approximation coefficients for each of approximate equations that respectively yield approximate values of electromagnetic characteristic values, between a plurality of elements constituting an electric circuit device and of the elements themselves, at an arbitrary frequency; and b) calculating the approximate values of the electromagnetic characteristic values between the elements and of the elements themselves at a designated frequency in accordance with the approximate equations having the approximation coefficients calculated in step a), thereby making it possible to evaluate the electromagnetic field intensity for the designated frequency.